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In mathematical finite group theory, an exceptional character of a group is a character related in a certain way to a character of a subgroup. They were introduced by , based on ideas due to Brauer in . ==Definition== Suppose that ''H'' is a subgroup of a finite group ''G'', and ''C''1, ..., ''C''''r'' are some conjugacy classes of ''H'', and φ1, ..., φ''s'' are some irreducible characters of ''H''. Suppose also that they satisfy the following conditions: #''s'' ≥ 2 #φ''i'' = φ''j'' outside the classes ''C''1, ..., ''C''''r'' #φ''i'' vanishes on any element of ''H'' that is conjugate in ''G'' but not in ''H'' to an element of one of the classes ''C''1, ..., ''C''''r'' #If elements of two classes are conjugate in ''G'' then they are conjugate in ''H'' #The centralizer in ''G'' of any element of one of the classes ''C''1,...,''C''''r'' is contained in ''H'' Then ''G'' has ''s'' irreducible characters ''s''1,...,''s''''s'', called exceptional characters, such that the induced characters φ''i'' * are given by :φ''i'' * = ε''s''''i'' + ''a''(''s''1 + ... + ''s''''s'') + Δ where ε is 1 or −1, ''a'' is an integer with ''a'' ≥ 0, ''a'' + ε ≥ 0, and Δ is a character of ''G'' not containing any character ''s''''i''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exceptional character」の詳細全文を読む スポンサード リンク
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